intrarenal hemodynamics in with essential...

421

Intrarenal Hemodynamics in Patients WithEssential Hypertension

Genjiro Kimura, Masahito Imanishi, Toru Sanai, Yuhei Kawano, Shunichi Kojima,Kaoru Yoshida, Hitoshi Abe, Terunao Ashida, Hiroki Yoshimi, Minoru Kawamura,

Morio Kuramochi, and Teruo Omae

Intrarenal hemodynamics were estimated clinically in essential hypertension. Two-week studieswere performed in 30 patients with essential hypertension who were given a regular sodium diet inthe first week and a sodium-restricted diet in the second week. Intrarenal hemodynamic parameterssuch as afferent arteriolar (preglomerular) resistance, efferent arteriolar resistance, and glomer-ular hydrostatic pressure were calculated from renal clearances and plasma total proteinconcentration measured on the last day of the regular sodium diet. Calculations were based on

Gomez's equations with the assumption that the gross filtration coefficient ofglomerular capillarieswas normal. The increase in afferent arteriolar resistance (8,100±500 dyne.sec.cm-5) was signifi-cantly correlated with an elevation in mean arterial pressure (120+2 mm Hg), whereas glomerularpressure (56± 1 mm Hg) and efferent arteriolar resistance (2,500+100 dyne.sec.cm-5) remainednormal. The renal function curve (pressure-natriuresis relation) was drawn by plotting urinarysodium excretion on they axis as a function of mean arterial pressure on the x axis, both of whichwere measured on the last 3 days ofeach week. The extrapolated x intercept (107±2 mm Hg) of therenal function curve was strongly correlated in a 1:1 fashion with the sum of the arterial pressure

drop from the aorta to the renal glomeruli plus the opposing pressures against glomerular filtrationat glomeruli (r=0.7, p<0.001) on the regular sodium diet, suggesting that the difference betweenmean arterial pressure on the regular sodium diet and the extrapolated x intercept represented theeffective filtration pressure across the glomerular capillaries on the regular sodium diet. The grossfiltration coefficient of glomerular capillaries was estimated as 0.154±0.018 (mllsec)/mm Hg,suggesting that the filtration coefficient was not affected in essential hypertension. Our resultsindicate that Gomez's equations can be applied to patients with essential hypertension. Further-more, it is suggested that intrarenal hemodynamics can be estimated independently of Gomez'sequations by analyzing the renal function curve. (Circulation Research 1991;69:421-428)

O n the basis of animal experiments, Brenner etal1-3 recently proposed that an abnormalityof intrarenal hemodynamics plays a key role

in the progression of renal failure. However, intrare-nal hemodynamics such as afferent and efferent arte-riolar resistances and glomerular hydrostatic pressurecannot be evaluated clinically except by Gomez'sequations,45 where the gross filtration coefficient ofglomerular capillaries must be assumed to be normal.

From the Department of Medicine, National CardiovascularCenter, Suita, Osaka, Japan.Supported by research grants from the Osaka Kidney Founda-

tion (OKF89-0003) and the Cardiovascular Research Foundationand Metabolic Disorders Treating Foundation and a grant for"Progressive Renal Disease" from "Specially Selected Diseases bythe Ministry of Health and Welfare Research Project," theMinistry of Health and Welfare of Japan.Address for reprints: Dr. Genjiro Kimura, Chief, Division of

Nephrology, National Cardiovascular Center, 5-7-1 Fujishiro-dai,Suita, Osaka 565, Japan.

Received September 5, 1990; accepted April 1, 1991.

Thus, it is impossible to examine whether Brenner'shypothesis1-3 can also be applied to clinical settings,since the gross filtration coefficient should be reducedin renal failure.6'7 In the present study, we estimatedintrarenal hemodynamics in patients with essentialhypertension by Gomez's equations and by analyzingtheir interrelation with the renal function curve (pres-sure-natriuresis relation).8'9

Materials and MethodsPatients

Thirty inpatients with essential hypertension (17 menand 13 women; 40-69 years old [average, 52±1 years];body weight, 63.0+2.0 kg; height, 160.0+1.4 cm), whohad given their informed consent, were studied in theHypertension Unit of the National CardiovascularCenter Hospital in Osaka, Japan. The administration ofantihypertensive drugs was discontinued at least 2weeks before hospitalization. During the initial hospi-

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422 Circulation Research Vol 69, No 2 August 1991

talization, a routine examination of hypertensive pa-tients was performed to exclude secondary hyperten-sion and to evaluate the severity of the hypertensivestate. None had evidence of detectable cause for hy-pertension or malignant hypertension.

Study ProtocolAfter the initial 1-2-week hospitalization, during

which blood pressures had been stabilized, the pa-tients were studied in the following two stages. First,they were fed a regular sodium diet containing 12-15g NaCl (205-256 meq sodium)/day for 1 week (stageI). Then, they were fed a low sodium diet containing1-3 g NaCl (17-51 meq sodium)/day for the nextweek (stage II). During these 2 weeks, no antihyper-tensive drugs were administered.The blood pressures and urinary sodium excretion

rate (UNaV) were measured on the last 3 days of eachstage. Blood pressure in the supine position wasmeasured by nurses three times each day at about10:00 AM after the patients rested for at least 30minutes, and the lowest value was adopted. Themean arterial pressure (MAP) was calculated byadding one third of the pulse pressure to the diastolicpressure, both of which were the averages of the last3 days of measurements.On the last day of stage I, blood hematocrit value

(Hct) and plasma total protein concentration (TP)were measured. The renal plasma flow rate (RPF) andglomerular filtration rate (GFR) were calculated bystandard clearance techniques5 using para-aminohip-purate and endogenous creatinine as markers, respec-tively. Patients fasted overnight and rested in thesupine position during measurements of renal clear-ances. A bolus intravenous injection of 5 ml of 10%para-aminohippurate was given at about 8:30 AM fol-lowed by the continuous infusion at a rate of 5 ml/hr.After a 30-minute equilibration period, two 30-minuteurine collections were performed. Venous blood sam-pling for plasma para-aminohippurate and creatininedeterminations was drawn at the beginning and end ofeach urine collection period. The renal clearance data,obtained by averaging the above two 30-minute clear-ances, were standardized for a body surface area of 1.73mi2. The renal blood flow rate (RBF) was calculatedfrom RPF and Hct.

Intrarenal hemodynamics were calculated basedon Gomez's equations4,5,10-14 (see "Appendix") usingclinical data such as MAP, RPF, GFR, Hct, and TP.The renal function curve (pressure-natriuresis rela-tion)8-10,15,16 was drawn by plotting UNaV on they axisas a function of MAP on the x axis; both variableswere measured after a steady-state sodium balancehad been achieved on regular and low sodium diets.The interrelation between intrarenal hemodynamicsand the renal function curve was studied. The theo-retical background of the interrelation is described indetail in "Appendix." Finally, intrarenal hemody-namics were calculated also by analyzing the renalfunction curve and were compared with those ob-tained by Gomez's equations.

TABLE 1. Blood Pressures and Urinary Sodium Excretion in 30Patients With Essential Hypertension on Regular and LowSodium Diets

Regular sodium diet Low sodium dietMeasurements (stage I) p (stage II)UNaV (meq/day) 223±10 <0.001 30±3SBP (mm Hg) 163±2 <0.001 143±3DBP (mm Hg) 98±2 <0.001 92+2MAP (mmHg) 120±2 <0.001 109±2

Values are mean±SEM. UNdV, urinary sodium excretion rate;SBP, DBP, MAP, systolic, diastolic, and mean blood pressure ofsystemic circulation, respectively.

Statistical AnalysisResults are expressed as mean+SEM. The signif-

icance of difference was tested by Student's t test forpaired samples, and the correlation coefficient wasobtained by the least-squares method. The signifi-cance of difference from 1 in the slope of theregression line and from 0 in the y intercept wastested by SAS/STAT Statistical Software Package (SASInstitute Inc., Cary, N.C.).

ResultsUrinary Sodium Excretion and Blood PressureUNaV and blood pressures were measured during

regular (stage I) and low (stage II) sodium diets in 30patients with essential hypertension, and the resultsare summarized in Table 1. When sodium intake wasrestricted from the regular to low sodium diet, UNaVwas decreased from 223±10 to 30±3 meq/day, re-flecting the amount of sodium intake in each stageand indicating that a steady state of sodium balancehad been achieved. Systolic blood pressure, diastolicblood pressure, and MAP of systemic circulationwere all lowered significantly by sodium restriction.

Renal Clearances, Hematocrit, and Plasma ProteinGFR, RPF, RBF, Hct in systemic blood, and TP

in systemic plasma were measured on the regularsodium diet (stage I), and the results are summa-rized in Table 2.

Renal Function CurveThe renal function curve (arterial pressure-UNaV

relation) was obtained by plotting UNaV (meq/day) instages I and II on the y axis as a function of MAP(mm Hg) on the x axis (Figure 1). The extrapolated xintercept (A) and the slope (B) of the renal functioncurve were 107±2 mm Hg and 23.4±2.4 (meq/day)/

TABLE 2. Renal Clearances, Hematocrit, and Plasma TotalProtein Concentration on Regular Sodium Diet

GFR RPF RBF Hct TP(mllmin) (mI/min) (mVmin) (%) (g/dl)85±3 377+15 666±27 43.2±0.7 6.8±0.1Values are mean±SEM (n=30). GFR, glomerular filtration

rate; RPF, renal plasma flow rate; RBF, renal blood flow rate; Hct,hematocrit value of systemic blood; TP, total protein concentra-tion in systemic plasma.



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Kimura et al Intrarenal Hemodynamics in Hypertension 423

W

E

> 100 /

100 110 120

MAP (mmHg)

FIGURE 1. Renal function curve (pressure-natriuresis rela-tion) in essential hypertension. The extrapolated x intercept ofthe curve, 107±2 mm Hg, represents the theoretically criticalblood pressure level at which urinary sodium excretion (UNaV)stops with the decrease in systemic bloodpressure. MAP, mean

arterial pressure.

mm Hg, respectively, indicating a theoretical UNaV ofzero when systemic MAP was lowered to approxi-mately 107 mm Hg and a change in systemic MAP(1/B) of 4 mm Hg per 100 meq/day change in thesodium intake.

Intrarenal HemodynamicsAccording to Gomez's equations (see "Appen-

dix"),4'5 the intrarenal hemodynamic parameters in 30patients with essential hypertension on the regularsodium diet (stage I) were calculated using clinicaldata such as MAP, renal clearances, and TP, whichhave been summarized in Tables 1 and 2. The grossfiltration coefficient of glomerular capillaries (KFG)was assumed to be normal (0.0812 [ml/secd/mm Hg).5Total renal vascular resistance (RT), afferent arterio-lar resistance (RA), and efferent arteriolar resistance(RE) were calculated as 13,900+700, 8,100+500, and2,500+-- 100 dyne.sec-cm5, respectively (Table 3). Themean glomerular pressure (PG) was 56±1 mm Hg,which is similar to the normal value of 60 mm Hg.4'5These results were comparable with those of theoriginal works by Gomez.4

Relations between segmental renal vascular resis-tances (RA or RE) and renal clearances (RPF, GFR,or filtration fraction that is equal to GFR/RPF) were

examined. RPF was reduced with increases in bothRA (r=-0.852, p<0.001) and RE (r=-0.680,p<0.01). On the other hand, GFR decreased with theincrease in RA (r=-0.479, p<0.01), while it in-creased with the increase in RE (r=0.370, p<0.05).Thus, filtration fraction was increased with increasesin both RA (r=0.551, p<0.01) and RE (r=0.939,p<0.001). It was notable that RA correlated stronglywith RPF, and RE correlated strongly with filtrationfraction.

Relations between segmental renal vascular resis-tances and systemic arterial pressure were also ex-

amined. RA was increased even in patients whoseblood pressure was normal, and the increase in RAwas positively correlated with an elevation in MAP(r=0.6, p<0.01), while RE remained normal and hadno significant relation with MAP (r=0.3, NS). Simi-larly, PG remained normal and was not correlatedwith MAP (r=0.02, NS). Thus, autoregulatory mech-anisms seemed almost intact in these essential hyper-tensive patients; the increases in RA and MAP wereparallel, and therefore, PG remained normal.

Interrelation Between Intrarenal Hemodynamics andRenal Function Curve

Since the x intercept of the renal function curve(A) is the theoretically critical blood pressure level atwhich urinary sodium excretion stops with the reduc-tion in MAP,8,9 the difference between MAP on theregular sodium diet and A (MAP-A) may corre-spond to the effective filtration pressure across theglomerular capillaries on the regular sodium diet. Inother words, when urinary sodium excretion stopswith the reduction in MAP, MAP should be loweredto A, and at the same time, glomerular filtration muststop because of the zero effective filtration pressure.Thus, A may correspond to the sum of the arterialpressure drop from the aorta to the renal glomeruliplus the pressures opposing glomerular filtration atthe glomerulus on the regular sodium diet, as shownby Equation A15 in "Appendix":

A=RAX RBF/1,328+(HT+H-IG)

TABLE 3. Intrarenal Hemodynamics Estimated by Gomez's Equations and by Analyzing Renal Function Curve

By Gomez's By analyzing renalequations p function curve

RA (dyne.sec-cm-5) 8,100+500 <0.01 8,600+500RE (dyne-sec-cm-5) 2,500+100 ...

RE' (dyne-sec-cm 5) 5,800+200 <0.01 5,300+300PG (mm Hg) 56±1 <0.005 52+1KFG ([mlsec]/mm Hg) 0.0812 0.154±0.018

(assumed constant)

Values are mean+SEM (n=30). RA, afferent arteriolar resistance; RE, efferent arteriolar resistance; RE', an

approximate of RE obtained as the difference between total renal vascular resistance and RA; PG, glomerularhydrostatic pressure; KFG, gross filtration coefficient of glomerular capillaries.



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from the aor

pressures agai)regular sodiunthese two, suJfiltration presMAP is the nsodium diet. RRBF, renal EBowman's spcular capillarie.

where HT iispace (assunoncotic presmated in eathe mass cothe glomeruas shown byIn Figure 2.plotted on tlof the equalated by Gorof this regrecantly diffeiintercept (mmHg (p>pendently o:RBF, theretwo (r=0.72arbitrary asMAP on theto the effectular capillarthere was amm Hg, p<RAX RBF/1,Once it h;

sponds apprsure, the K,estimated fro

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"Appendix." The estimated KFG was 0.154+0.018(ml/sec)/mm Hg, which was nearly twice as great asthe assumed value of 0.0812.5 This is because A wassignificantly greater than RAxRBF/1,328+(HT+IIG)by 4.5+ 1.4 mm Hg and MAP-A seemed smallerthan the true value of effective filtration pressure bythis magnitude. These results indicate that KFG is notdecreased in essential hypertension and that Go-mez's equations4'5 can be applied to patients withessential hypertension.

Estimation of Intrarenal Hemodynamics by AnalyzingRenal Function Curve

-r =0.724 (n=30) Once it has been established that MAP-A corre-p< 0.001 sponds approximately to the effective filtration pres-

______,_____,_____,_____,_____,____ sure across the glomerular capillaries on the regular90 100 110 120 130 sodium diet, as shown in Figure 2, RA can be

RAXRBF/1328+ (HT+TTG) (mmHg) estimated by analyzing the renal function curve byrearranging Equation A15 in "Appendix." Thus, an(elation between the x intercept of the renal approximate (RE') of the efferent arteriolar resis-(A) and the sum of the arterial pressure drop tance can be obtained as the difference between the

ta to the renal glomeruli plus the opposing total renal vascular resistance and RA. The glomeru-nstglomerularfiltration at the glomerulus on the lar hydrostatic pressure (PG) can be estimated as the'i diet. There was a strong 1:1 relation between difference between systemic arterial pressure and theggesting that MAP-A represents the effective pressure drop along afferent arteriole from aorta tosure across the glomerular capillaries, where glomeruli, which corresponds to RAxRBF/1,328. Ta-nean systemic arterial pressure on the regular ble 3 compares the intrarenal hemodynamic param-?A, afferent arteriolar (preglomerular) resistance; eters estimated by analyzing the renal function curve5lood flow rate; HT, hydrostatic pressure in with those by Gomez's equations. Since the RA2ce; IIG, mean oncotic pressure within glomer- estimate was significantly higher by the renal functionS. curve than by Gomez's equations, the RE' and PG

estimates were lower. Figure 3 shows the correlationssthe hydrostatic pressure in Bowman's in RA, RE', and PG between these two methods ofned to be 10 mm Hg) and 11G is the mean estimation. The slopes of these regression lines,isure within glomerular capillaries (esti- 0.930±0.075 in RA (p>0.358) and 0.798+0.143 invch patient as 28.9+±0.4 mm Hg based on RE' (p>0.170) were not significantly different from 1,tnservation law of plasma protein across nor were they intercepts, 1,120+ 639 dyne.sec.cm `inJlar capillaries using TP, RPF, and GFR RA (p>O.090) and 622±+856 dyne-sec.cm-5 in RE'Equations A3 and A4 in "Appendix"). (p>0.474), different from 0 dyne.sec.cm-. There,the left side of this equation (A) was were highly significant 1:1 correlations in RA and RE'he ordinate as a function of the right side between these two methods of estimation, and thus,Ltion (RAXRBF/1,328+[HT+IIG]) calcu- no correlation in PG. Therefore, it seemed possible tonez's equations4'5 on thex axis. The slope estimate RA and RE' clinically by analyzing the renal.ssion line (0.818±0.151) was not signifi- function curve. Of course, there was a significantrent from 1 (p>0.238), nor was its y correlation (r=0.512,p<0.01) between RE' estimated23.0±+15.5 mm Hg) different from 0 by the renal function curve and RE by Gomez's>0.149). Although A was obtained inde- equations (RE'=2,100+1.25 x RE). No correlation intf the other parameters, such as RA and PG should be ascribed to the fact that PG is autoreg-was a strong 1:1 relation between these ulated within a narrow range. Furthermore, it should1, p<O.OOl), suggesting the validity of the be emphasized here that if we assume KFG to be;sumption that the difference between 0.154±0.018 instead of 0.0812 (ml/sec)/mm Hg inregular sodium diet andA corresponded each patient, then we get exactly the same results byive filtration pressure across the glomer- Gomez's equations as by analyzing the renal functionies on the regular sodium diet. However, curve (see Figure 4). The observed difference (Tablesmall but significant difference (4.5 + 1.4 3) between results obtained by Gomez's equations0.005) between A (107±+2 mm Hg) and and by analyzing the renal function curve is ascribed328+(HT+IIG) (102±2 mm Hg). only to the difference in KFG.as been established that MAP-A corre-^oximately to the effective filtration pres- DiscussionFG of glomerular capillary walls may be By relating intrarenal hemodynamics with the re-om its definition by using Equation Al in nal function curve (pressure-natriuresis relation),

.041

2



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0, 15,000

Uc

RA t 10,000,dyns.sec.cm-5) E

c5,000

.0 01

- ~ * S

0

- 0 S Y=1,100+0.93X0

ir =0.924 (n=30)000 P<0.0010/- 0

---1 '5,000 10,000 15,000

by Gomez's Equations

70-

PG(mmHg) 601-

50

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0r_ciU

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(dyns.sec.cm5) =

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10,000 -

8,000 [

6,000 [

4,000

0

0

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* * z Y=600,>0 r =0.72

P<O.OO

4,000 6,000 8,000 10,000by Gomez's Equatdons

(mmHg) «^.0

80

70

60

4,000

0 0

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1.

50 Nt* r=0.078 (n =501~~~~~~a0

40 50 60 70 80

by Gomez's Equations

FIGURE 3. Relations in afferent arteriolar resistance (RA), an

approximate (RE') of efferent arteriolar resistance, and glo-merular hydrostatic pressure (PG) between two methods ofestimation by Gomez's equations and by analyzing the renalfunction curve. There were significant 1 :1 relations in RA andRE', but no correlation was found in PG RE' was obtained as

the difference between total renal vascular resistance and RA.

the validity of the underlying assumptions in Gomez'sequations4,5 for calculating intrarenal hemodynamicsusing clinical data has been clarified. Furthermore, itis suggested that intrarenal hemodynamics can beestimated clinically by analyzing the renal functioncurve without assuming a normal and constant gross

filtration coefficient of glomerular capillaries.Our results on intrarenal hemodynamics in 30

patients with essential hypertension were consistentwith those of the original works by Gomez.4 Amongtotal renal vascular resistances, the preglomerular(afferent) arteriolar resistance was prominently ele-vated, and thus, the glomerular pressure remainednormal. Reasonable relations between segmental re-nal vascular resistances, afferent or efferent (post-glomerular), and renal clearances observed in thepresent study, although they are all interdependent,may also suggest the validity of Gomez's equations4,5as well as of our data concerning intrarenal hemody-

=30)

RE3,000

(dyns-sec-cm-5) 2,000

1,000

nL4~3 I I _

0.05 0.10 0.15

KFG ((mi/sec) /mmHg)0.20

FIGURE 4. Effects of the errors in gross filtration coefficientofglomerular capillaries (KFG) on the estimation of intrarenalhemodynamics by Gomez's equations. When KFG is increased,glomerular hydrostatic pressure (PG) and efferent arteriolarresistance (RE) are reduced while afferent arteriolar resistance(RA) increased. Here, measured values such as glomerularfiltration rate, renal blood flow, and mean arterial pressure

were kept constant.

namics. RPF was reduced by both afferent andefferent arteriolar vasoconstriction, whereas GFRwas decreased with the increase in the afferentarteriolar resistance and was increased with theincrease in the efferent resistance. Estimation ofintrarenal hemodynamics by Gomez's equations4'5requires two major assumptions, as summarized in"Appendix." First, in the estimation of glomerularhydrostatic pressure by Gomez's equations, KFG mustbe assumed. Here, we assumed normal value of KFGin patients with essential hypertension. In spontane-ously hypertensive rats, which is a model of humanessential hypertension, the filtration coefficient ofsingle nephron was reported as normal, and afferentarteriolar resistance was prominently increased withan elevation in systemic blood pressure, resulting innormal glomerular pressure.1718 These data werealso comparable with those observed in essential

RA

1+0.80X25 (n=30))l

-41 A-

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1

4

A A A



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hypertensive patients in the present study. Recently,we used Gomez's equations to analyze intrarenalhemodynamics in patients with unilateral renovascu-lar hypertension11 and found them completely com-parable with those reported in the Goldblatt ratmodel.19,20 Second, filtration disequilibrium is as-sumed in Gomez's equations. However, it is notknown yet whether filtration equilibrium is achievedat the end of the human glomerular capillaries.Therefore, as far as we know, there are no exactformulas to calculate intrarenal hemodynamics inhumans. Fortunately, in dogs and rats there were nosignificant differences between conclusions derivedby Gomez's disequilibrium model and by the filtra-tion equilibrium model.12-14 Using dextran sievingdata, Shemesh et a16 and Tomlanovich et a17 at-tempted to assess glomerular hemodynamics in hu-mans. They concluded that KFG is reduced in bothmembranous nephropathy6 and diabetic glomerulop-athy.7 In their assessment, however, the effectivefiltration pressure must be assumed.6,7 Therefore, itseems difficult to quantitatively assess intrarenal he-modynamics such as glomerular pressure, afferentarteriolar resistance, and efferent arteriolar resis-tance calculated in the present study.

Furthermore, interrelations between intrarenalhemodynamics and the renal function curve werestudied. Since the x intercept (A) of the renal func-tion curve represents the theoretically critical bloodpressure level at which urinary sodium excretionstops with the decrease in systemic arterial pres-sure,89 MAP-A seems to be the effective filtrationpressure across the glomerular capillary walls on theregular sodium diet. Therefore, A may be expressedas the sum of the arterial pressure drop from theaorta to the renal glomeruli, mainly in the afferentarteriole, plus opposing pressures against glomerularfiltration at the glomerulus as shown by EquationA15 in "Appendix." Figure 2 revealed that there wasa 1:1 relation between A and the sum, both of whichwere estimated independently of each other by therenal function curve and by Gomez's equations,respectively, although A was slightly greater than theother. This small difference (4.5±1.4 mm Hg,p<O.OOS) may be ascribed to the fact that the renalfunction curve is not truly linear. Linking two datapoints, where the steady-state MAP and UNaV undertwo different amounts of sodium intake were plottedon the x and y axes, respectively, and calculating theextrapolated A might give us a value greater than thetrue value. However, we still believe that the renalfunction curve can be regarded as linear in clinicalpractice as we have discussed in detail elsewhere.15Since there was a strong 1:1 relation between A andthe sum of the arterial pressure drop from the aortato glomeruli plus opposing pressures against glomer-ular filtration despite the small difference, we believethat A can be used to estimate approximately theeffective filtration pressure across the glomerularcapillary walls in clinical studies. In the present study,

A15 in "Appendix," under the conditions in whichafferent arteriolar resistance mainly varied. It isreported that the relation holds when the oncoticpressure within glomerular capillaries primarily var-ies.21,22 The renal function curve was shifted leftward(A was decreased) when the oncotic pressure wasreduced,21 while it was shifted rightward (A wasincreased) by increasing the oncotic pressure.22Once it has been established that MAP-A corre-

sponds approximately to the effective filtration pres-sure across the glomerular capillaries on the regularsodium diet, the KFG of glomerular capillary walls canbe estimated from its definition using the estimatedeffective filtration pressure, MAP-A, and GFR. Theestimated KFG, 0.154+0.018 (ml/sec)/mm Hg, wasnearly twice the assumed value of 0.0812,5 reflectingthe small difference between MAP-A and the truevalue of the effective filtration pressure, discussedabove. It seems that KFG is not affected, at least notdecreased, in essential hypertension as assumed byGomez.4 Thus, it is suggested that Gomez's equationscan be applied to calculating intrarenal hemodynam-ics in patients with essential hypertension. If KFG isknown to be 0.154±0.018 (ml/sec)/mm Hg from anal-ysis of the renal function curve, then intrarenal hemo-dynamic parameters can be calculated. Intrarenalhemodynamics calculated by analyzing the renal func-tion curve were comparable with those obtained byGomez's equations (Table 3), indicating that they canbe estimated without assuming KFG.

In animal experiments, Brenner et al'-3 recentlyshowed the importance of intrarenal hemodynamics inthe progression of renal failure. However, there is noway to evaluate intrarenal hemodynamics in clinicalsettings except by Gomez's equations.4'5 Thus, Gomez'soriginal report4 itself has not been reevaluated untilnow. Furthermore, KFG is assumed normal in Gomez'sequations,45 making it even more difficult to applythem to the disease processes of renal failure. Therenal function curve may be useful to estimate intrare-nal hemodynamics quantitatively in clinical settings,especially when we want to see mainly the changes inintrarenal hemodynamics instead of the absolute val-ues.'0 The present study may enable us to examinewhether intrarenal hemodynamics play an importantrole in the progression of renal failure in humans, asBrenner proposed in animal models, by analyzing therenal function curve. For example, the relatively infre-quent occurrence of renal failure despite systemichypertension in essential hypertension as seen inspontaneously hypertensive rats3'17,18 may be ascribedto the normal glomerular pressure due to afferentvasoconstriction. Since direct measurements of intra-renal hemodynamics are impossible in humans atpresent, there is no direct way to clarify the validity ofour indirect estimation. Further studies are clearlyrequired before our method can be applied to clinicalpractice. We hope that our present approach willstimulate further studies to analyze intrarenal hemo-

we tested the validity of the above relation, Equation dynamics in clinical settings.



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AppendixSummary of Gomez's EquationsGomez4 reported in detail how to estimate quan-

titatively intrarenal hemodynamics using clinical datasuch as systemic MAP, GFR, RPF, RBF, and TP.Introduced by Smith,5 Gomez's equations are sum-marized briefly here to make it easier to understandtheir underlying principles as well as the presentstudy.

First, in Gomez's equations, the intrarenal vascularresistances are functionally divided into three compo-nents: preglomerular (afferent, RA), postglomerular(efferent, RE), and venular. Second, the hydrostaticpressures in venules, interstitium, renal tubules, andBowman's space within kidneys are considered to be inequilibrium and are given a value of 10 mm Hg. Third,the KFG of glomerular capillaries is assumed normal(0.0812 [ml/secl/mm Hg). From the above assumptions,the following equations are derived:

GFR=KFGXAPF (A1)

APF=PG-(HT+HG) (A2)where APF, PG, HT, and HG (mm Hg) are the effectivefiltration pressure across the glomerular capillaries,glomerular hydrostatic pressure, hydrostatic pressurein Bowman's space (assumed to be 10 mm Hg), andoncotic pressure within glomerular capillaries, re-spectively. GFR is expressed in milliliters per secondper 1.73 m2. 11G can be obtained knowing the meanconcentration (CM) of plasma protein within glomer-ular capillaries:

I1G=5X(CM-2) (A3)CM can be calculated on the basis of mass conserva-tion law of plasma protein during glomerular ultra-filtration using TP in systemic plasma and filtrationfraction, FF (=GFR/RPF).

TP 1CM=-X lOge (4

FF 1-FF (A4)

Solving Equations Al-A4, PG can be estimated as

GFR TP 1PG= +HT+5x -xloge- -2 (A5)

Once PG is known, the following equation can bederived from Ohm's law:

RAXRBF (A6)MAP-PG= 1,328

Here, the number 1,328 is the conversion factor.Finally, the afferent arteriolar resistance can becalculated as

RA=MAP PGX 1,328 (A7)RBFDl

Similarly, the efferent arteriolar resistance can beobtained as

GFRRE=KFGX(RBF-GFR)

xl ,328 (A8)

Since KFG must be assumed in Gomez's equations,the effects of the errors in KFG on the estimation ofintrarenal hemodynamics were analyzed using Equa-tions A5, A7, and A8 (Figure 4). Here, the measuredvalues such as GFR, RBF, and MAP were keptconstant. When KFG is increased, PG and RE arereduced and RA is increased.

Determination of the Renal Function CurveAssuming that the relation between arterial pres-

sure and urinary sodium excretion rate is linear, therenal function (pressure-natriuresis) curve wasdrawn by linking two data points obtained in a steadystate under two different amounts of sodium intake(regular and low) in each patient, where MAP(mm Hg) and UNaV (meq/day) were plotted on the xandy axes, respectively. The extrapolatedx intercept,A (mm Hg), and the slope, B ([meq/day]/mm Hg),were calculated as follows10,15,16:

UNaV(I)XMAP(II)-UNaV(II)XMAP(I)UNaV(I)-UNaV(1I)

UNaV(I)-UNaV(II)B=

MAP(I-MAP(II)

(A9)

(A10)

where I and II refer to the data obtained in a steadystate under regular (stage I) and low (stage II)sodium diets, respectively. Using A and B, UNaV cannow be expressed as a function of MAP:

UNaV=B x(MAP-A) (All)

Interrelation Between Intrarenal Hemodynamics andRenal Function CurveThe renal function curve, expressed as Equation

All, shows that when MAP is lowered to A, urinaryoutput stops. That is, the x intercept of the renalfunction curve, A, is the theoretically critical bloodpressure level at which urinary sodium excretionstops with the decrease in MAP.8,9 The mechanismsof the stop of urinary sodium excretion with thereduction in MAP to A should be ascribed to the stopof glomerular ultrafiltration. Therefore, when MAPis lowered to A, the APF across the glomerularcapillaries must be reduced to zero, resulting in thestop of glomerular filtration. Thus, 1MAP-A seems tocorrespond to APF on the regular sodium diet:

APF=MAP-A (A12)Since APF can be expressed as Equation A2, fromEquations A2 and A12 we get

PG-(HT+HIG)=MAP-A (A13)



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Furthermore, by rearranging Equation A6, the glo-merular hydrostatic pressure can be expressed as

RAX RBFPG=MAP-- 1,328 (A14)

Finally, by comparing Equations A13 and A14, weget the following important relation:

RAXRBFA= 1328 +(HT+HG) (A15)

1,328

This equation means that the x intercept of the renalfunction curve may be expressed as the sum of thepressure drop from aorta to glomeruli along afferentarteriole plus the opposing pressures against glomer-ular filtration at the glomerulus on the regular sodiumdiet. It must be noted that the values of A, RA, RBF,and HG are all obtained on the regular sodium diet.Since A and RA vary with systemic arterial pressure,all parameters must be measured on the same condi-tions. The above calculation is a form of the functionalstop-flow method and seems similar to the originalstop-flow method by which the glomerular hydrostaticpressure was first estimated by Gerz.23

References1. Brenner BM, Meyer TW, Hostetter TH: Dietary protein

intake and the progressive nature of kidney disease: The roleof hemodynamically mediated glomerular injury in the patho-genesis of progressive glomerular sclerosis in aging, renalablation, and intrinsic renal disease. N Engl J Med 1982;307:652-659

2. Brenner BM: Hemodynamically mediated glomerular injuryand the progressive nature of kidney disease. Kidney Int1983;23:647-655

3. Anderson S, Brenner BM: Role of intraglomerular hyperten-sion in the initiation and progression of renal failure, inKaplan BM, Brenner BM, Laragh JH (eds): The Kidney inHypertension. New York, Raven Press, Publishers, 1987, pp

67-764. Gomez DM: Evaluation of renal resistances, with special

reference to changes in essential hypertension. J Clin Invest1951;30:1143-1155

5. Smith HW: The Kidney: Structure and Function in Health andDisease. New York, Oxford University Press, Inc, 1951

6. Shemesh 0, Ross JC, Deen WM, Myers BD: Nature of theglomerular capillary injury in human membranous glomerulop-athy. J Clin Invest 1986;77:868-877

7. Tomlanovich S, Deen WM, Jones HW III, Schwartz HC,Myers BD: Functional nature of glomerular injury in progres-sive diabetic glomerulopathy. Diabetes 1987;36:556-565

8. Guyton AC: Arterial Pressure and Hypertension, CirculatoryPhysiology III. Philadelphia, Pa, WB Saunders Co, 1980

9. Guyton AC: Renal function curve: A key to understanding thepathogenesis of hypertension. Hypertension 1987;10:1-6

10. Kimura G, Deguchi F, Kojima S, Ashida T, Yoshimi H, AbeH, Kawano Y, Yoshida K, Kawamura M, Imanishi M, Sanai T,Kuramochi M, Omae T: Effect of a calcium entry blocker,nicardipine, on intrarenal hemodynamics in essential hyper-tension. Am J Kidney Dis 1991;17:47-54

11. Kimura G, London GM, Safar ME, Kuramochi M, Omae T:Glomerular hypertension in renovascular hypertensivepatients. Kidney Int 1991;39:966-972

12. Hall JE, Guyton AC, Cowley AW Jr: Dissociation of renalblood flow and filtration rate autoregulation by renin deple-tion. Am J Physiol 1979;232:F215-F221

13. Hall JE, Coleman TG, Guyton AC: Control of glomerularfiltration rate by circulating angiotensin II. Am J Physiol1981;241:R190-R197

14. Kobrin I, Pergram BL, Frohlich ED: Acute pressure increaseand intrarenal hemodynamics in conscious WKY and SHRrats. Am J Physiol 1985;249:H1114-H1118

15. Kimura G, Saito F, Kojima S, Yoshimi H, Abe H, Kawano Y,Yoshida K, Ashida T, Kawamura M, Kuramochi M, Ito K,Omae T: Renal function curve in patients with secondaryforms of hypertension. Hypertension 1987;10:11-15

16. Kimura G, Deguchi F, Kojima S, Ashida T, Yoshimi H, AbeH, Kawano Y, Yoshida K, Imanishi M, Kawamura M,Kuramochi M, Omae T: Antihypertensive drugs and sodiumrestriction: Analysis of their interaction based on pressure-na-triuresis relationship. Am J Hypertens 1988;1:372-379

17. Arendshorst WJ, Beierwaltes WH: Renal and nephron hemo-dynamics in spontaneously hypertensive rats. Am J Physiol1979;236:F246-F251

18. Azar S, Johnson MA, Scheiman J, Bruno L, Tobian L:Regulation of glomerular capillary pressure and filtration ratein young Kyoto hypertensive rats. Clin Sci 1979;56:203-209

19. Schwietzer G, Gertz KH: Changes of hemodynamics andglomerular ultrafiltration in renal hypertension of rats. KidneyInt 1979;15:134-143

20. Steiner RW, Tucker BJ, Gushwa LC, Gifford J, Wilson CB,Blanz RC: Glomerular hemodynamics in moderate Goldblatthypertension in the rat. Hypertension 1982;4:51-57

21. Manning RD Jr: Effects of hypoproteinemia on renal hemo-dynamics, arterial pressure, and fluid volume. Am J Physiol1987;252:F91-F98

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23. Gerz KH, Mangos JA, Baun G, Pagel HD: Pressure in theglomerular capillaries of the rat kidney and its relation toarterial pressure. Pfiugers Arch 1966;288:369-374

KEY WORDS * renal hemodynamics * renal circulationrenal vascular resistance * filtration coefficient * glomerularhypertension * arterial pressure-natriuresis relation * essentialhypertension



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Yoshimi and M KawamuraG Kimura, M Imanishi, T Sanai, Y Kawano, S Kojima, K Yoshida, H Abe, T Ashida, H

Intrarenal hemodynamics in patients with essential hypertension.

Print ISSN: 0009-7330. Online ISSN: 1524-4571 Copyright © 1991 American Heart Association, Inc. All rights reserved.is published by the American Heart Association, 7272 Greenville Avenue, Dallas, TX 75231Circulation Research

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